The customer help center in your company receives calls from customers who need help with some of the customized software solutions your company provides.Previous studies had indicated that 20% of customers who call the help center are Hispanics whose native language is Spanish and therefore would prefer to talk to a Spanish-speaking representative.This figure coincides with the national proportion, as shown by multiple larger polls.You want to test the hypothesis that 20% of the callers would prefer to talk to a Spanish-speaking representative.You conduct a statistical study with a sample of 35 calls and find out that 11 of the callers would prefer a Spanish-speaking representative.The significance level for this test is 0.01.The value of the test statistic obtained is:
A)0.008
B)0.29
C)0.58
D)1.69
E)1.73

Question

Quizplus · Accepted Answer

The test statistic for a proportion is calculated using the formula $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and $n$ is the sample size. Here, $\hat{p} = \frac{11}{35}$, $p_0 = 0.20$, and $n = 35$. Plugging these values into the formula gives a test statistic of approximately 1.69.

The Customer Help Center in Your Company Receives Calls from Customers